Sample Space

A Sample space is the list of all outcomes in a random experiment.      

Simulation

When it is impossible to list all
the outcomes, we create a model of the experiment.  This is called simulation.

Experimental definition of  Probability

By simulating the experiment,  we
will find the number of times a particular event or outcomes occur out of the
total number of trials.  Based on this
we have a new definition of probability called Experimental definition of
Probability



Experimental Probability Formula

Let us consider a random experiment. 
Let A be an outcome of the random experiment .  Then A is called an event. 
The Experimental probability of the event A is given by
                P(A) = Number of times the event occurs/ Total number of trials
Experimental probability is also known as Relative frequency
definition of Probability.

Lets consider a few examples
Example 1: -
A die is thrown 100 times out of which 5 appears 28 times.  Find the experimental probability of getting  the number 5?
Solution: -                                       
 The Experimental probability of the event A is given by
                P(A) = Number of times the event occurs/ Total number of trials
Here die is thrown 100 times.  So total number of trails =100
The number 5 occurs 28 times. So the number of times the required event
occurs = 28
Therefore probability of getting  the number 5 = 28/100 = 0.28
 

Example 2: -
A Box contains 15 red balls, 12 blue balls and 13 green
marbles. Find the experimental probability of getting a green ball.
Solution: -            
The Experimental probability of the event A is given by
                P(A) = Number of times the event occurs/ Total number of trials
Take a ball from the box. Note the color and return the ball.
Repeat a few times (maybe 200 times). Note the number of times a green ball
was picked (Suppose it is 120).
The experimental probability of getting a green ball from
the box is 120/200 = 60/100 = 0.6


Example 3: -
The following are the marks obtained by 1200 students in
a particular examination.
Marks:             100-120      120-140         140-160       160-180       180-200          
No of                   63               142                   500           320                  175 
Students
Find the probability that a student selected has marks
(i) under 140
(ii) above 180
(iii) between 140 and 200
Solution: -
The Experimental probability of the event A is given by
                P(A) = Number of times the event occurs/ Total number of trials
We can see that the total of the marks is 63 + 142 + 500 + 320 + 175 = 1200
(i) We have to find the probability that a selected student get marks under 40.
There are 63 + 142 = 205 students getting marks under 140.              
Therefore P(student getting marks under 140)= 205/1200 = 0.17
(ii)  We have to find the probability that a selected student get marks above 180.
There are 175 students getting marks above180.                
Therefore P(student getting marks above 180) = 175/1200 = 0.15
(iii)   We have to find the probability that a selected student get marks between 140 and 200.
There are 500 + 320 + 175 = 995 students getting marks between 140 and 200.  Therefore P(student getting marks between 140 and 200) = 995/1200 = 0.83